Question

applying the triangle inequality theorems and the converse of the pythagorean theorem
classify each of the triangles as acute, obtuse, or right.
triangle jkl is △ triangle.
triangle xyz is △ triangle.
(the image shows triangle jkl with sides jk=4, kl=3, jl=6 and triangle xyz with sides xy=5, yz=4, xz=4)

Explanation:

Step1: Identify longest side of △JKL

Longest side $JL=6$, others $JK=4, KL=3$

Step2: Compare $c^2$ to $a^2+b^2$ for △JKL

Calculate $6^2=36$, $4^2+3^2=16+9=25$. Since $36>25$, the triangle is obtuse.

Step3: Identify longest side of △XYZ

Longest side $XY=5$, others $YZ=4, XZ=4$

Step4: Compare $c^2$ to $a^2+b^2$ for △XYZ

Calculate $5^2=25$, $4^2+4^2=16+16=32$. Since $25<32$, the triangle is acute.

Answer:

Triangle JKL is obtuse triangle.
Triangle XYZ is acute triangle.